The Three Lions coach Gareth Southgate admitted he wants the player to get more game time at United but admitted: "It's not my business to interfere with club managers".
Romelu Lukaku has been United's undisputed first-choice striker since arriving in a £75 million deal from Everton in the summer of 2017, leaving Rashford to get the majority of his first-team minutes from the substitutes' bench or starting on the wing.
Rashford did not do his chances of starting the next game any favours though last time out at Burnley after being sent off for a headbutt on Phil Bardsley.
And Sutton believes the United youth product, who burst onto the scene in 2016, should leave Old Trafford and find somewhere where he is the main man. "He's got huge competition for places at his club, so you can understand [his frustration]".
"He's a huge admirer of him, but he's got his job to do".More news: Emiratis in U.S. warned as Hurricane Florence approaches east coast
Daily Telegraph columnist Jamie Carragher made the point that Rashford has the most hard of tasks at United - a young player coming through as a striker at a big club.
However, at club level, his season has been far from ideal.
The Mirror has reported that following the victory over Switzerland, Southgate suggested Rashford's performances for England would boost his confidence and emphasised that he was still an emerging player with world-class potential. They have to try to win matches.
"The people that (are) speaking about his minutes, I think they are a bit confused", he concluded at the end of the question. "For me, I was delighted because we really wanted to make him feel important over this period anyway".More news: Hurricane Florence Produces Wind Gusts Near 100 miles per hour in Eastern North Carolina
"Some of the step-overs and things Cristiano Ronaldo was doing at that age [were remarkable], but Ronaldo wasn't converting them into the same number of goals".
"It's not my business to interfere with club managers, they have a hard job to do and they have big squads at the top six, huge competition for places, so Jose thinks the world of Marcus", he said.
Mourinho's side will be looking to end Watford's ideal start in the new campaign in a Premier League match set for Vicarage Road.
"It's not my business to interfere with club managers, they have a hard job to do and they have big squads at the top six, huge competition for places, so Jose thinks the world of Marcus", Southgate said.More news: China welcomes United States invitation for new round of trade talks